Conquest started his career with Prahran in 1899, playing there until July 1900 when he retired due to ill-health. He then enlisted to fight with the 5th Victorian Mounted Rifles in the Boer War in February 1901. He returned to Australia in April 1902, playing another season with Prahran before joining Melbourne. He waited a year before making his league debut as a rover/half-forward after suffering a leg injury in May 1903.

After 17 games in his first season, Conquest had to wait until Round 5 to start his 1905 campaign after an ankle injury in the last training session before Round 1. In 1907 he played for the St Kilda team in the Wednesday League.

In 1909 he returned to Prahran for a third time, and worked as a groundsman for the MCC. That year, while working at the Warehouseman's Ground (today's Albert Ground), he was attacked, knocked unconscious and robbed of seven pounds.

He joined South Australian side Sturt in 1911, but wasn't cleared and could only play in practice games. He finally won his freedom in 1912 and appeared in three games for them.